## Describe the y-intercept and end behavior of the following graph: The graph starts on the top left and curves down to the

Question

Describe the y-intercept and end behavior of the following graph:

The graph starts on the top left and curves down to the right, crosses the x axis at negative 2, then crosses the y axis at negative 4 and continues decreasing to the bottom right.

(−2, 0); The graph approaches y = −6 to the right.
(0, −5); The graph approaches y = −6 to the right.
(−2, 0); The graph decreases to the left.
(0, −5); The graph decreases to the left.

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3 weeks 2021-09-24T18:41:21+00:00 2 Answers 0

Based on graph description …

• end behavior: (-∞, +∞), (+∞, -∞)
• y-intercept: (0, -4)

Based on what appear to be answer choices …

• end behavior: (-∞, ∞), (+∞, -6)
• y-intercept: (0, -5)

Step-by-step explanation:

End behavior

“Starts at top left” means the function approaches +∞ as x approaches -∞.

“Continues decreasing to the bottom right” seems to mean the function approaches -∞ as x approaches +∞.

(While an exponential decay function “continues decreasing”, it approaches a limit. Your description of the graph says nothing about that, so we assume it is an odd-degree polynomial function with a negative leading coefficient.)

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Y-intercept

“Crosses the y axis at negative 4” means the y-intercept is (0, -4).

_____

Comment on problem statement discrepancies

Perhaps you intended to describe the graph as “approaching -6 at the bottom right.” That would match a description, “The graph approaches y = −6 to the right.” However, your offered choice of (0, -5) for the y-intercept does not match the verbal description of “crosses the y axis at negative 4.”